A048851 Length of hypotenuse squared in right triangle formed by a prime spiral plotted in Cartesian coordinates.

8, 13, 34, 74, 170, 290, 458, 650, 890, 1370, 1802, 2330, 3050, 3530, 4058, 5018, 6290, 7202, 8210, 9530, 10370, 11570, 13130, 14810, 17330, 19610, 20810, 22058, 23330, 24650, 28898, 33290, 35930, 38090, 41522, 45002, 47450, 51218, 54458

Offset: 1

Author

Enoch Haga

Keywords

• easy
• nonn

Examples

			a(2) = 13 because c^2 = a^2 + b^2 = 4 + 9 = 13.
		

References

• H. E. Huntley, The Divine Proportion, A Study in Mathematical Beauty. New York: Dover, 1970. See Chapter 13, Spira Mirabilis, especially Fig. 13-5, page 173.

Crossrefs

Cf. A006094.

Formula

To begin prime spiral, plot (2, 0), (0, 2). Square of hypotenuse is c^2 = a^2 + b^2, or 8 = 4 + 4, so a(1) = 8.

a(n) = A069484(n-1), n >= 2. - Mamuka Jibladze, Mar 24 2017